Because the concept of depolarization confuses students that have not had physiology, I have added this simplistic explanation. If you understand membrane potential and depolarization, there is no need to read it. If you do read it and find it confusing, please let me know so that I may improve it.

The potential difference across the plasma membrane of human cells varies between -20 mv (millivolts) and -200 mv depending upon the cell type.  The potassium ion concentration is much higher inside the cell than it is outside the cell (see Table 4.1: 150 mM vs.4 mM).  Most of the membrane potential is due to the leakage of potassium from inside the cell membrane to the outside of the membrane.  As potassium ions, K+, move from their high concentration inside of the cell membrane to a lower concentration outside of the cell membrane, they carry a positive charge with them.  This movement causes the inside of the cell to be negative with respect to the outside of the cell.

The movement of most of the K+ is through potassium channels.  If the movement of K+ ions through the potassium channels is inhibited, the inside of the cell membrane becomes less negative with respect to the outside.  For example, the potential difference might change from a -80 mv to -20 mv.  This is called depolarization.  The depolarization is due to the leakage of other positive ions like sodium into the cell.

ATP in B-cells binds to K-channels and inhibits them.  Less K+ moves through the membrane and the cells become depolarized.  That is, the resting membrane potential drops from -80 mv toward zero. 

Calcium channels are opened as the membrane potential moves from a -80 mv toward zero.  That is, as long as the resting membrane potential is maintained, no calcium channels are opened but when the membrane potential drops below a certain negative value, the calcium channels are opened.  This causes calcium, whose concentration is 10,000 time higher outside the cell membrane than inside the cell membrane, to rush into the cell. The change in calcium ion concentration is dramatic.

The increase is calcium ion causes a series of reactions to occur.  The end result is that the insulin vesicles fuse with the cell membrane and their contents are released into the intercellular space.

ATP-sensitive potassium (KATP) channels, so named because they are inhibited by intracellular ATP, play key physiological roles in many tissues. In pancreatic β cells, these channels regulate glucose-dependent insulin secretion and serve as the target for sulfonylurea drugs used to treat type 2 diabetes.